Algebra 1 Common Core Student Edition, Grade 8-9

Go t I t? 1. What are the solutions of each equation?

a. (x + l) ( x - 5) = 0 b. (2x + 3 ) ( x — 4 ) = 0

C. (2y + l) ( y + 14) = 0 d. (7« - 2 )(5 /i - 4) = 0

How can you factor
x2 + 8x + 15?
Find tw o integers w ith a
product of 15 and a sum
of 8.

You can also use the Zero-Product Property to solve equations of the form

ax2 + bx + c = 0 if the quadratic expression ax2 + bx + c can be factored.

So l v i n g b y Fa ct o r i n g

Multiple Choice What are the solutions of the equation x2 + 8x + 15 = 0?

(3D -5 , -3 CD -3 , 5

QD -5 ,3 CD 3,5

x2 + 8x + 15 = 0

( x + 3 ) ( x + 5 ) = 0 Factor x 2 + 8x + 15.

x + 3 = 0 o r x + 5 = 0 Use the Zero-Product Property,

x = - 3 o r x = —5 Solve fo r x.

Ihe solutions are —3 and —5. Ihe correct answer is A.

Go t I t? 2. What are the solutions of each equation?

a. m2 — 5m — 14 = 0 b. p2 + p — 20 = 0 c. 2a2 - 15a + 18 = 0

Think
Why do you need
to subtract 18 from
each side before you
factor?
To use th e Zero-P roduct
Property, one side of the
e q u a tion m u st be zero.

Before solving a quadratic equation, you may need to add or subtract terms from

each side in order to write the equation in standard form. Then factor the quadratic

expression.

I W r i t i n g i n S t a n d a r d F o r m F i r s t

What are the solutions of 4x2 - 21x = 18?

4x2 — 21x = 18

4 x 2 - 2 1 x - 1 8 = 0 Subtract 18 from each side.

( 4 x + 3 ) ( x - 6 ) = 0 Factor 4 x 2 - 21x - 18.

4 x + 3 = 0 o r x - 6 = 0 Use the Zero-Product Property.

4x=-3 o r x = 6 Solve fo r x.

3

* = "4 or x = 6

Ihe solutions are — j and 6.

®°t It? 3. a. What are the solutions of x2 + 14x = —49?

b. Reasoning Why do quadratic equations of the form x2 + 2ax + a2

or xz — 2ax + a2 = 0 have only one real-number solution?

c

PowerAlgebra.com | Lesso n 9- 4 Fact oring t o Solve Quad rat ic Eq uat io ns